A simple complementary framework for evaluating evaporation base on land-atmosphere coupling

Evaporation (E) is a key process in land-atmosphere water and energy exchanges. Among the evaporation methods, the complementary relationship (CR) approach builds upon the dynamic feedbacks of water and heat fluxes between the land-atmosphere interface, providing a straightforward framework for estimating evaporation using basic meteorological inputs, without relying on complex land surface information. Although CR is a simple and effective method, traditional CR mechanisms/models still face two main challenges. First, the wet boundary condition of CR is inaccurately characterized. When the land surface is not water-limited, evaporation is defined as potential evaporation (E_po). However, E_po estimates using conventional methods often do not align with its fundamental definition, as meteorological variables observed under real conditions differ from those over a hypothetical wet surface. Here, we estimate E_po using the maximum evaporation approach (E_{po_max}) that does follow the original E_po definition. Our findings show that using E_{po_max} significantly reduces the asymmetry in the CR. Second, traditional CR mechanisms focus on the feedback between water vapor and temperature in the land-atmosphere system, while overlooking the impact of these changes on radiation. As the surface transitions from dry to wet, enhanced actual evaporation and reduced sensible heat flux lead to cooler and wetter air above the surface, reducing the vapor pressure deficit and further decreasing atmospheric evaporative capacity (or apparent potential evaporation, E_pa). Building on this, we found temperature reduction overall increases the radiation term in E_pa and partially offsets the traditional view that water vapor weakens the aerodynamic term. Based on the above modifications, we developed a physically-based, calibration-free CR model, which requires few input variables and thus facilitates evaporation estimation. More importantly, the CR method, grounded in land-atmosphere coupling, offers a simpler framework for studying the feedback of evaporation on climate, making it a promising tool compared to complex coupled climate models.